{"title":"关于包含在一点上的三个2乘2的平面的法诺变换的不合理性","authors":"Elisabetta Ambrogio , Daniela Romagnoli","doi":"10.1016/S1385-7258(89)80012-5","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that the Fano variety <em>W</em> of degree 6 in ℙ<sup>5</sup>, complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of ℙ<sup>5</sup>, is not rational if it contains 3 planes two by two meeting at least in one point.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 1","pages":"Pages 15-19"},"PeriodicalIF":0.0000,"publicationDate":"1989-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80012-5","citationCount":"0","resultStr":"{\"title\":\"On the non-rationality of the Fano variety of ℙ5, which contains three planes two by two meeting in one point\",\"authors\":\"Elisabetta Ambrogio , Daniela Romagnoli\",\"doi\":\"10.1016/S1385-7258(89)80012-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove that the Fano variety <em>W</em> of degree 6 in ℙ<sup>5</sup>, complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of ℙ<sup>5</sup>, is not rational if it contains 3 planes two by two meeting at least in one point.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"92 1\",\"pages\":\"Pages 15-19\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80012-5\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1385725889800125\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800125","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the non-rationality of the Fano variety of ℙ5, which contains three planes two by two meeting in one point
We prove that the Fano variety W of degree 6 in ℙ5, complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of ℙ5, is not rational if it contains 3 planes two by two meeting at least in one point.
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